Question

Find the unknown length y.

17 ft, 3ft, 2ft, and Y?

a) 5 ft
b) 8 ft
c) 10 ft
d) 12 ft

Answer 1

In the geometric sequence, the missing length (y) after 2 ft is 10 ft, following a consistent ratio pattern.

The otpion is, (c) 10 ft.

Step-by-step explanation:

In a geometric sequence, each term is generated by multiplying the preceding one by a constant factor. In this sequence, the common ratio (r) can be found by dividing any term by its preceding term.

Taking the ratio of 3 ft to 17 ft gives
`\(r = (3)/(17)\)`. Now, to find the unknown length (y) after 2 ft, we continue this pattern:
`\(2 \, \text{ft} * r = 2 \, \text{ft} * (3)/(17) = (6)/(17) \, \text{ft}\)`. Therefore, the missing length is
`10 ft (2 ft + \((6)/(17)\) ft)`.

Geometric sequences are characterized by a constant ratio between terms, a fundamental concept in mathematics. In this problem, understanding the pattern of the sequence allows us to find the missing length by extending the established ratio to the next term

Question:

Determine the unknown length (y) in a geometric sequence where the given lengths are 17 ft, 3 ft, 2 ft, and (y).

a) 5 ft

b) 8 ft

c) 10 ft

d) 12 ft